John A. Boehner has said he wants to "clean the barn" of some unfinished legislative business before he steps down, and on Wednesday the speaker's team confirmed that could include a deal to avoid a financial default by the federal government.

"The speaker has made it clear that he wants to solve some outstanding issues before he leaves," a Boehner aide told CQ Roll Call. "No decisions have been made, but a resolution on the debt ceiling is certainly possible." The comment came amid reports that Boehner, who had originally intended to step down at the end of the month, is working on a bill to raise the debt limit before the nation run out of cash next month.

The Congressional Budget Office provided an update Wednesday on its debt limit breach projections, saying that it came in response to questions from members of Congress.

"By CBO's estimate, the Treasury would most likely be able to continue borrowing and have sufficient cash to make its usual payments through sometime in the first half of November without an increase in the debt limit," the nonpartisan office said. "Earlier or later dates are possible, depending on the amount and timing of cash flows in the next several weeks."

That brings CBO's findings roughly into alignment with the most recent update from Treasury Secretary Jacob J. Lew, who told Boehner and other congressional leaders that extraordinary measures are likely to be exhausted during the first week of November.

In previous debt limit debates, Boehner has asked that cooler heads in the House Republican Conference prevail in efforts to extract concessions from the Democrats and the Obama administration as a condition of raising the debt limit. The Ohio Republican likely sees it in the best interest of his party to stick around until the matter can be dealt with, working closely as he has in the past with Senate Majority Leader Mitch McConnell, R-Ky.

McConnell has said repeatedly that there will be no shutdowns or debt limits breaches on his watch.

Senate Majority Whip John Cornyn, R-Texas, told CQ Roll Call in a recent interview that while he agreed with conservatives that certain policy concessions are desirable in exchange for raising the debt ceiling, the U.S. cannot afford to go over the cliff.

“We can’t do that," Cornyn said. "We can’t do that. We need to deal with the problem."